When using real tube rectifiers (3B28 and such) I delay the HV for 30sec and then I have a resistor in series with caps that is shorted about 30sec after HV.
So, use a double timer in series to make sure the rectifiers only get HV when hot and that the start is always smooth.
With the rest of the rectifiers, just find one slow enough for the circuit you're using

One project I did was set up with separate heater and HV supplies. I designed it that way since it used SS for the HV DC, and the circuit incorporated DC coupling between stages (ist preamp to LTP phase splitter/2nd pre and cathode follower grid drivers to the finals). This way, the heaters could be warmed up before the HV is switched on so that Vhk ratings aren't exceeded when the HV appears while cathodes are still cold.

In that case, the HV is interrupted if the heaters aren't switched on first. No heater power, no HV. This system worked out just great, and the amp has not failed in almost daily use since 2005.

A different project used a multi-secondary PTX (6.3V @ 5.0A; 5.0V @ 3.0A; 650Vct @ 150mA) with a 5U4GB for the HV. (Needed 350Vdc, and the PTX overvolted badly with SS diodes -- it looks like it was designed (NOS) to provide ~350Vdc when used with 5U4GBs, as that's what the plate characteristic predicted, and what I got once the PS was built.) With this project, there is just the one power switch that powers up everything: heaters and HV DC. Again, no problems with this design, as the HV DC is delayed anyway.